I think the first line offers a very generic prophecy of "the hope of elves and men". The line which follows makes that prophecy much more specific by saying that "a new star shall rise". A lot of descendants or accomplishments could be characterized as "hope" but the Star of Earendil is the only "new star" in the recorded history of Middle Earth.

I think the primary meaning of Hurin's words is Earendil, although a secondary meaning is that the "hope of elves and men" continually springs from Earendil's line in the Second and Third ages.